Octuple-precision floating-point format: Difference between revisions

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Revision as of 19:34, 10 July 2025 edit 208.114.63.4 (talk) →Octuple-precision examples ← Previous edit		Latest revision as of 12:51, 3 August 2025 edit undo C.Fred (talk \| contribs) Autopatrolled, Administrators 282,201 edits m Reverted edit by 2A01:CB16:201A:C683:0:67:3AB1:9A01 (talk) to last version by Vincent Lefèvre Tag: Rollback
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Line 51: of the floating-point value. This includes the sign, (biased) exponent, and significand. ~~8000~~ 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000<sub>16</sub> = −0+0▼ ~~<pre<includeonly></includeonly>>~~ ~~0000~~ 8000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000<sub>16</sub> = +0−0 ▲8000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000<sub>16</sub> = −0 ~~</pre>~~ ~~ffff~~ 7fff f000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000<sub>16</sub> = ~~−infinity~~+infinity▼ ~~<pre<includeonly></includeonly>>~~ ~~7fff~~ ffff f000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000<sub>16</sub> = ~~+infinity~~−infinity ▲ffff f000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000<sub>16</sub> = −infinity ~~</pre>~~ 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0001<sub>16</sub>▼ ~~<pre<includeonly></includeonly>>~~ = 2<sup>−262142</sup> × 2<sup>−236</sup> = 2<sup>−262378</sup>▼ ▲0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0001<sub>16</sub> ≈ 2.24800708647703657297018614776265182597360918266100276294348974547709294462 × 10<sup>−78984</sup>▼ ▲= 2<sup>−262142</sup> × 2<sup>−236</sup> = 2<sup>−262378</sup> (smallest positive subnormal number)▼ ▲≈ 2.24800708647703657297018614776265182597360918266100276294348974547709294462 × 10<sup>−78984</sup> ▲ (smallest positive subnormal number) ~~</pre>~~ 0000 0fff ffff ffff ffff ffff ffff ffff ffff ffff ffff ffff ffff ffff ffff ffff<sub>16</sub>▼ ~~<pre<includeonly></includeonly>>~~ = 2<sup>−262142</sup> × (1 − 2<sup>−236</sup>)▼ ▲0000 0fff ffff ffff ffff ffff ffff ffff ffff ffff ffff ffff ffff ffff ffff ffff<sub>16</sub> ≈ 2.4824279514643497882993282229138717236776877060796468692709532979137875392 × 10<sup>−78913</sup>▼ ▲= 2<sup>−262142</sup> × (1 − 2<sup>−236</sup>) (largest subnormal number)▼ ▲≈ 2.4824279514643497882993282229138717236776877060796468692709532979137875392 × 10<sup>−78913</sup> ▲ (largest subnormal number) ~~</pre>~~ 0000 1000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000<sub>16</sub>▼ ~~<pre<includeonly></includeonly>>~~ = 2<sup>−262142</sup>▼ ▲0000 1000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000<sub>16</sub> ≈ 2.48242795146434978829932822291387172367768770607964686927095329791378756168 × 10<sup>−78913</sup>▼ ▲= 2<sup>−262142</sup> (smallest positive normal number)▼ ▲≈ 2.48242795146434978829932822291387172367768770607964686927095329791378756168 × 10<sup>−78913</sup> ▲ (smallest positive normal number) ~~</pre>~~ 7fff efff ffff ffff ffff ffff ffff ffff ffff ffff ffff ffff ffff ffff ffff ffff<sub>16</sub>▼ ~~<pre<includeonly></includeonly>>~~ = 2<sup>262143</sup> × (2 − 2<sup>−236</sup>)▼ ▲7fff efff ffff ffff ffff ffff ffff ffff ffff ffff ffff ffff ffff ffff ffff ffff<sub>16</sub> ≈ 1.61132571748576047361957211845200501064402387454966951747637125049607182699 × 10<sup>78913</sup>▼ ▲= 2<sup>262143</sup> × (2 − 2<sup>−236</sup>) (largest normal number)▼ ▲≈ 1.61132571748576047361957211845200501064402387454966951747637125049607182699 × 10<sup>78913</sup> ▲ (largest normal number) ~~</pre>~~ 3fff efff ffff ffff ffff ffff ffff ffff ffff ffff ffff ffff ffff ffff ffff ffff<sub>16</sub>▼ ~~<pre<includeonly></includeonly>>~~ = 1 − 2<sup>−237</sup>▼ ▲3fff efff ffff ffff ffff ffff ffff ffff ffff ffff ffff ffff ffff ffff ffff ffff<sub>16</sub> ≈ 0.999999999999999999999999999999999999999999999999999999999999999999999995472▼ ▲= 1 − 2<sup>−237</sup> (largest number less than one)▼ ▲≈ 0.999999999999999999999999999999999999999999999999999999999999999999999995472 ▲ (largest number less than one) ~~</pre>~~ 3fff f000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000<sub>16</sub>▼ ~~<pre<includeonly></includeonly>>~~ = 1 (one)▼ ▲3fff f000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000<sub>16</sub> ▲= 1 (one) ~~</pre>~~ 3fff f000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0001<sub>16</sub>▼ ~~<pre<includeonly></includeonly>>~~ = 1 + 2<sup>−236</sup>▼ ▲3fff f000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0001<sub>16</sub> ≈ 1.00000000000000000000000000000000000000000000000000000000000000000000000906▼ ▲= 1 + 2<sup>−236</sup> (smallest number larger than one)▼ ▲≈ 1.00000000000000000000000000000000000000000000000000000000000000000000000906 ▲ (smallest number larger than one) ~~</pre>~~ By default, 1/3 rounds down like [[double precision]], because of the odd number of bits in the significand.